Average Error: 0.1 → 0.1
Time: 23.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r6205563 = x;
        double r6205564 = y;
        double r6205565 = sin(r6205564);
        double r6205566 = r6205563 * r6205565;
        double r6205567 = z;
        double r6205568 = cos(r6205564);
        double r6205569 = r6205567 * r6205568;
        double r6205570 = r6205566 + r6205569;
        return r6205570;
}
↓
double f(double x, double y, double z) {
        double r6205571 = y;
        double r6205572 = cos(r6205571);
        double r6205573 = z;
        double r6205574 = x;
        double r6205575 = sin(r6205571);
        double r6205576 = r6205574 * r6205575;
        double r6205577 = fma(r6205572, r6205573, r6205576);
        return r6205577;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))